By the AEP
[1]},
\(& & \Pr \lbrace \mathcal {E}_{1}^{c}(1,1)|\mathcal {K}_{1}\rbrace  & \le \epsilon ,&\\& & \Pr \lbrace \mathcal {E}_{1}(w_2,j_2)|\mathcal {K}_{1}\rbrace &\le 2^{-n[I(U;Y_1)-\epsilon ]}, \quad \text{for} ~w_2\ne 1,&\\&\text{and}&\Pr \lbrace \mathcal {E}_{1,1}(w_1,j_1,1,1)|\mathcal {K}_{1}\rbrace &\le 2^{-n[I(X;Y_1|U)-\epsilon ]}, \quad \text{for} ~w_1\ne 1.&\) 
